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Stability of the Linearized Transient Semiconductor Device Equations
Author(s) -
Markowich P. A.,
Ringhofer Ch. A.
Publication year - 1987
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19870670710
Subject(s) - eigenvalues and eigenvectors , semigroup , discretization , mathematics , transient (computer programming) , mathematical analysis , stability (learning theory) , biasing , upper and lower bounds , semiconductor device , singular perturbation , exponential stability , perturbation (astronomy) , euler's formula , control theory (sociology) , physics , computer science , voltage , quantum mechanics , materials science , nonlinear system , machine learning , artificial intelligence , composite material , operating system , control (management) , layer (electronics)
Abstract We present a stability analysis of the linearized transient semiconductor device equations by means of semigroup theory. Central to the developed theory is an estimate for the real parts of the eigenvalues of the linearized device problem with an upper bound which only depends on the biasing situation of the device. Under realistic assumptions we show that the device problem and its implicit Euler time discretisation are uniformly (with respect to an intrinsic singular perturbation parameter) stable ‘in the linearized sense’.